Trust-based trade

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SEMINARIOS DE ALMOÇO

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FUNDAÇÃO

DA EPGE

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GETULIO VARGAS

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Trust-Based Trade

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EMANUEL ORNELAS

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(University of Georgia)

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Data: 01/07/2005 (Sexta-feira)

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Horário: 12 h 15 min

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Local:

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Praia de Botafogo, 190 - 110 _andar

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FGV

Auditório nO 1

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Coordenação:

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EPOE

Praf. luis Henrique B. Braido

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e-mail: Ibraido@fgv.br

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Thust-Based Trade

Luis Araujo and Emanuel Ornelas*

May 2005

Abstract

There is substantially more trade within national borders than across borders. An important

･ｸｰｬｾｮ｡ｴｾｯｮ＠ for this fact is the weak enforcement of international contracts. We develop a model in which agents build reputations to overcome this institutional failure. The model describes the

interplay between institutional quality, reputations and the dynamics of international trade. It

also rationalizes several empirical regularities. We find that history matters for trade volumes, but that its effects vary with the institutional setting of the country. The same is true for the efticacy of trade liberalization programs. Moreover, while stricter enforcement of contracts enhances trade in the short run, it makes it harder for individual traders to develop good reputations. We show that this indirect negative effect may produce an "institutional trap": for sufliciently low initial levels of contract enforcement, a small tightening in enforcement reduces future trade fiows. We find also that search frictions aggravate the problems created by weak enforceability of contracts, even if they impose no direct cost on agents. The model allows extensions in several directions. We outline two of them, indicating how one could study transnational networks and the effects of firm heterogeneity within our structure.

JEL Classification: FIO, F23, D83, Ll4

Key Words: International trade, Export dynamics, Contract enforcement, Reputation

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"While performance is the glue of buyer-seller relationships, the trust that is built as partners gain experience with each other is the lubricant." [Egan and Mody 1992, p. 326]

1

Introduction

Countries trade too little with each other relative to what they trade with themselves. An expla-nation for this fact is the weakness of contract enforcement across interexpla-national jurisdictions. As Rodrik (2000, p. 179) argues, "Transaction costs arise from various sources, but perhaps the most obvious is the problem of contract enforcement. When one of the parties reneges on a written contract, local courts may be unwilling-and international courts unable--to enforce a contract signed between residents of two different countries. Thus, national sovereignty interferes with con-tract enforcement, leaving international transactions hostage to an increased risk of opportunistic behavior." Since rational agents anticipate that possibility, they trade less internationally than they do within national borders.

The primary motivation for our paper relies on the idea that Rodrik is right-i.e., the idea that contract enforcement is an important determinant of international transactions. We argue, furthermore, that traders build reputations within their relationships to mitigate the difficulties created by asymmetric information when international contracts are not properly enforced. In this context, our analysis characterizes how enforcement of contracts matters for international trade.

We develop a 2-country in complete information dynamic model, where potential exporters from one country form partnerships with distributors in the other country without knowing the type of each distributor. We show that weak enforcement of international contracts depresses international trade, but also facilitates the formation of reputations; the latter moderates the negative impact of weak enforcement on trade. Still, since the process of reputation building is time-consuming, the volume of international trade remains low relative to the leveIs attained when contracts are properly enforced. In this sense, reputation is a substitute for adequate contract enforcement, but an imperfect one. In the long run, however, reputations can become a perfect substitute for contract enforcement if distributors are sufficiently patient. That is, if a partnership between an exporter and a distributor goes on indefinitely, the reputation of the latter becomes eventually so high that it makes contract enforcement irrelevant within that partnership.

Our analysis shows that tightening the enforcement of contracts in a country would have a direct positive effect on trade but also an indirect negative effect, because it would slow down the process of reputation building. The net effect on trade flows within existing partnerships would then depend on both the horizon of the analysis and the initiallevel of contract enforcement. In the short run, when reputations are given, trade would increase for sure. However, future trade

flows would falI if the initial leveI of enforcement were too low, suggesting the existence of an "institutional trap." More generally, we show that the effect of stricter contract enforcement on trade flows is higher, the higher the initiallevel of enforcement. This indicates that there may be "increasing returns" to contract enforcement: the higher its current leveI, the greater the impact of increasing it on trade flows.

Additional results folIow when we incorporate search frictions into our basic setting. Search frictions are emphasized by Rauch and Trindade (2003), who consider an international economy in which agents in a country have imperfect information regarding the location of their best match in a foreign country. Similarly, we assume that when a producer searches for a distributor, he may meet with one who is incapable of distributing his good, in which case the producer does not export in that período In contrast with Rauch and Trindade, however, we model search as an essentialIy costless process, since we allow a producer to search for as many periods as he wants at no cost. Yet we find that search frictions aggravate the problem created by incomplete information about distríbutors' types, carrying it from the partnership leveI to the aggregate leveI. The reason is that distributors who honor contracts become available for a match only if their previous matches were with producers whose products they were unable to distribute. Myopic distributors, on the other hand, become available for that reason and also because they may have defaulted on contracts in a previous relationship. As a result, the average quality of the pool of distributors with whom producers can meet deteriorates continuously. EventualIy, the prior formed by potential exporters regarding their possible matches becomes so pessimistic that they stop searching, even though they know that some patient distributors are still available. Thus, with search frictions, the market does not replicate the perfect information equilibrium even in the long run.

We also show that while tariffs reduce the volume of trade in every period and in every part-nership, the magnitude of the reduction depends on the leveIs of both the reputation within the partnership and the country's leveI of contract enforcement. We find that, under certain conditions, trade liberalization is more effective in promoting trade within more mature partnerships, suggest-ing that history matters for the efficacy of trade liberalization. The effects of stricter contract enforcement on the effectiveness of trade liberalization programs, on the other hand, will generally depend on the initiallevel of contract enforcement.

N umerous case studies provide anecdotal support for our hypotheses that contract enforcement is important for international trade and that agents rely on trust when enforcement is not strict. For example, Woodruff (1998) documents the difficulties faced by exporters in Mexico's footwear industry seeking to enter foreign markets created by the high cost of taking legal actions abroad. Egan and Mody (1992, p. 327), through a series of interviews with D.S. entrepreneurs in the bicycle and footwear industries, find that "buyers consider trust an essential adjunct to formal

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legal agreements, and some even use trust as a substitute."

More recently, economists have begun to assess these issues more formally. Anderson and Marcouiller (2002), as well as Ranjan and Lee (2003), find strong evidence that (the lack of) contract enforcement is a key determinant of (observed low leveIs of) international trade flows. Izquierdo et aI. (2003) find, in turn, that firms' reputations in third countries are an important factor in explaining bilateral trade flows. And McMillan and Woodruff (1999), analyzing Vietnam, show forcefully how relationships based on trust arise and develop in environments where contract enforcement is virtually absent.1

The available evidence, therefore, appears to leave little doubt about the relevance of contract enforcement and of reputations for international trade. Yet there has been no formal theoretical analysis within the trade literature that integrates these two elements.2 _{Anderson (2003) and}

An-derson and Young (2003) recognize the obstacles created by ineffective enforcement of international contracts, but study instead countries' choices of enforcement leveIs. McLaren (1999) characterizes, in a static model, the circumstances under which firms choose to base their relationships on trust instead of on (enforceable) contracts. We abstract from the issues McLaren focuses on-industry structure and relationship-specific investments-to concentrate on the dynamics of trust within partnerships when perfectly enforceable contracts are unavailable. Chisik (2003) examines instead how the perception about producers from (otherwise identical) countries can become self-fulfilling and affect their choices of qualities, thus creating "reputational comparative advantages." Greif (1993), in turn, analyzes how limited contract enforceability and a precarious communications sys-tem induced medieval merchants to build coalitions based upon reputation to sustain trade. He considers, however, a complete information economy, and his main goal is to explain why merchants employed a system of collective, instead of individual, punishment for dishonest agents. None of these papers, however, analyzes the dynamic process in which firms engaged in international ex-change build reputations as a response to the imperfect enforceability of contracts.3,4

lMcMillan and Woodruff (1999) base their analysis on a survey of managers of Vietnamese private firms. Ac-cording to the survey, 91 percent of the managers believe they cannot rely on the courts to enforce contracts.

2In fact, in Anderson's (2004) survey of the nascent literature on the reactions to the problems created by the lack of adequate contract enforcement in international transactions, there is no reference to formal analyses of the role of reputations.

3Ghosh and Ray (1996) and Watson (2002) study agents' incentives to establish long-term relationships as well. Ghosh and Ray's context is one of a community with multiple agents who face informational asymmetries, while Watson considers a two-player repeated game environment with two-sided informational asymmetries. Institutional elements play no role in either analysis, however.

4In a different context, the literature on sovereign debt also studies the effect of reputational concerns, but on the incentives of governments to honor international contracts. See Eaton and Fernandez (1995) for a survey of that literature.

Interestingly, our results match very closely the qualitative findings of Johnson et al. (2002). Using surveys of manufacturing firms in transition economies, they find that the volume of trans-actions within partnerships grows steadily. Such a practice of "start small and increase quantities over time" appears to be very common among firms entering export markets (see e.g. Egan and Mody 1992). Here, we rationalize it by showing how each exporter increases exports as he becomes convinced that his distributor will not behave opportunistically. This practice has been explained also by Rauch and Watson (2003), in a setting with asymmetric information, costly search and buy-ers who need to make irrevbuy-ersible investments to train foreign supplibuy-ers. We show that, if contracts are not perfect1y enforced, firms may want to "start small" even when those last two elements are absent.

Johnson et al. (2002) find also that, while stricter enforcement of contracts has no clear effect on long-lasting partnerships, it boosts transactions within new partnerships. This is precisely what our model predicts: in the former case, reputations are already consolidated, so contract enforcement is pointless. In the later case, by contrast, there is still significant uncertainty about the types of distributors, so the short-run impact of stricter contract enforcement within partnerships is necessarily positive (even though its long-run effect may be negative, as indicated above). J ohnson et al. find as well that a better legal system induces the formation of more partnerships. While our basic model cannot predict entry, in an extended version in which firms have heterogeneous costs (discussed later in the paper), a stronger legal system would indeed prompt entry.

Our model rationalizes also Eichengreen and Irwin's (1998) finding that (aggregate) trade flows display hysteresis, as well as some strong empirical regularities documented by recent research on exporting behavior at the plant and firm leveI (see Tybout 2003 for a survey of that literature). Two robust findings in that line of research are that, for most industries, only a relatively small number of producers in a country export, and that a producer is more likely to export in a certain period if he exported in the previous period. The standard explanation for these phenomena is the existence of firms' sunk costs to begin exporting, but the precise nature of those costs remains unclear. Our model indicates that they reflect, at least partially, informational asymmetries and imperfect enforceability of contracts. It suggests, in addition, that the difliculties to begin exporting are market-specific, consistently with the findings of Eaton et al. (2004) that firms typically export to only a few markets. Our model, therefore, supports the use of measures of contract enforceability as proxies for (an inverse of) the sunk costs necessary to begin exporting to individual countries.

Our mo deI permits various extensions as well. We outline two of these possibilities. One is the role of business networks. In the presence of search frictions, networks among producers could help support international trade by spreading information about their previous experiences. In that context, one could analyze also the incentives to form international networks, an issue that has

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not yet been formally analyzed, as Rauch (2001) points out. The other potential extension that we suggest is the introduction of cost heterogeneity among producers. Cost heterogeneity could enrich significantly the dynamics of trade and would bring about a new dimension of the effects of trade policy.

The paper proceeds as follows. Section 2 describes the mode!. Section 3 analyzes the behavior of exporters. Section 4 analyzes the behavior of distributors and characterizes an equilibrium of the mode!. Section 5 describes the dynamics of trade, while Section 6 introduces search frictions. Implications for trade policy are discussed in Section 7. Possible extensions are outlined in Section 8. Section 9 concIudes.

2 Model

Our main goal is to study situations where the lack of contract enforcement depresses international trade. Such situations arise when exporters have to do business with agents in the importing çountry but cannot rely on the legal system to prevent opportunistic behavior by those agents. We develop an environment with these characteristics. It is based on three main elements, which we briefly discuss in turno

1. Contacting distributors

Contacting distributors in the importing country appears to be a criticaI decision in the process of exporting. According to the Home Based Business Opportunities, for example, "The most im-portant step in setting up your business is finding the contacts ... for commercial distribution." Similarly, the D.S. Department of Commerce (2000, p. 23) argues that once a "company is orga-nized to handle exporting, a proper channel of distribution needs to be carefully chosen for each market," while warning potential exporters that they "should investigate potential representatives or distributors carefully before entering into an agreement." We want to study precisely these types of situations, where exporters have to establish channels of distribution in the importing country, and have to do so cautiously, because distributors can behave opportunistically and will indeed do so if they have a relatively short horizon and are not inhibited by the legal system.

iL Credit-based relationships

We consider that exporters and distributors base their relationships on credito In particular, we assume that in each period an exporter consigns goods to a distributor, who has the opportunity to abscond with the full proceeds from the sales of the goods. In that event, the exporter has the option of suing the distributor to recover his due payment.

Commercial transactions are indeed largely based on credit.5 _{This approach is also}

particu-larly useful to study situations where export activities are subject to opportunistic behavior. We assume that, while exporters require distributors in the importing country to operate in that mar-ket effectively, an imperfectly functioning legal system makes them uncertain about whether the distributors wiH respect their formal agreements. Now, while there are many dimensions in which exporters may have to rely on agents in the importing country without fuH legal protection, al-lowing distributors to "run away" with the proceeds from their sales is arguably the simplest way to capture the possibility of opportunisticjdishonest behavior by those agents. Similarly, while enforcement of contracts matters in several dimensions of a business relationship, making sure bills are paid is perhaps the clearest among these situations.

iii. Measure of institutional quality

N aturally, the more lenient a country's legal system is in enforcing international contracts, the more easily distributors can evade contractually specified payments to exporters. There are different ways in which we can capture institutional quality in this contexto Ranjan and Lee (2003) and Anderson and Young (2003), for example, use a parameter to represent the proportion of contracts that the legal system enforces. In the sanie spirit, but more specifically, we measure the (lack of) quality of a legal system by the opportunities for corruption that it allows. At a general leveI, the gain of being corrupt is high when there is a lower risk of being caught. Accordingly, our measure of institutional quality corresponds to the measure À E (0,1) of non-corrupt(ible) legal agents in the importing country.

We now describe our environment in more detail.

2.1

Environment

Consider an economy with two countries, Rome and Foreign. In Rome there is a

[O,lJ

continuum of infinitely lived producers and a

[O,

1 J continuum of differentiated goods. Only one producer can manufacture each good, and marginal costs of production are constant at C. Producers can sell

goods in their own market directly, but have no direct access to Foreign's market. To become exporters, they need to form a partnership with a distributor from Foreign. Finally, they discount the future at a rate de, where Oe E (0,1)

5Interestingly, transactions are often based on credit even in environments where there is virtually no legal protec-tion, as McMillan and Woodruff's (1999) analysis of the business conditions in Vietnam c1early exemplifies: despite widespread skepticism about the effectiveness of the judicial system, over 50 percent of the business relationships in Vietnam involve trade credito

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In Foreign, there is a

[O,

1] continuum of infinitely lived agents with the ability to internally distribute imported goods. Distributors in Foreign can be either patient or myopic; the measure of myopic distributors is 00 • A patient distributor (p) is forward-Iooking with a discount factor

Ód E (0,1), while a myopic distributor (m) only maximizes current profits. The type of a distributor is his private information.

A producer always serves the local market. He can also become an exporter by searching for a distributor in Foreign in order to form a partnership. Meetings between producers and distributors are pairwise and happen once each period. When searching for a distributor, a producer faces an informational friction, since he does not observe the type of a distributor. To focus on the role played by information frictions, we initially assume that a producer from Home finds an agent in Foreign with the ability to distribute his good with certainty. In Section 6 we relax this assumption and consider the case where there are also search frictions.

Consider an ongoing partnership between an exporter and a distributor. In every period, the exporter decides whether to maintain the partnership. In this case, he proposes a contract to the distributor. Now, since distributors have incentives to build reputations only if contracts do not induce a separation between a myopic and a patient distributor, in what follows we restrict the class of contracts so that such separation is not possible during the contracting stage. More specifically, we assume that the exporter proposes a one-period contract6 _{to the distributor specifying the}

quantity to be exported but with an exogenous distribution of the revenue (say, the exporter and the distributor receive strictly positive fractions a and 1 - a of the revenue, respectively) and no si de payments. If the contract is accepted, the exporter produces the quantity specified in the contract, bears the production costs and pays a fixed cost /'i,

>

0.7 Otherwise, both the exporter and the distributor earn zero profits.

Note that these restrictions on possible contracts are driven mainly by our assumption that some distributors have strictly no concern about the future. With a more sophisticated description of these distributors, we could allow for a much broader range of contracts and still capture the dynamic incentives to build reputations.8 _{We nevertheless choose to model some distributors as}

6Such short-term contracts conform well to actual businesses practices. As Egan and Mody (1992, p. 326) report, "Relationships tend to grow incrementally, with their duration and depth more evident ex post than ex ante. A relationship often begins with a short-term agreement-perhaps a one-year production contract-and continues with annual renewals ... Thus, a dose, long-term relationship may arise with no more formal structure than a continuing series of renewed short-term contracts." Similarly, the D.S. Department of Commerce (2000, p. 28) points out that "some D.S. companies prefer to begin with a relatively short trial period and then extend the contract if the relationship proves satisfactory to both parties."

7This fixed cost captures in a simple way the exporter's opportunity cost to engage in business in Foreign. 80ne possibility is to have some distributors being, instead of myopic, of a behavioral type, in the sense that they

myopic-and then restrict contracts to a simple form-because this formulation uncovers the main ideas about reputation in a simpler and more direct way.

Now consider the problem of a distributor on whether to perform as the contract specifies or to default on the contract. Before making this decision, the distributor can randomly search for a legal agent in Foreign. Legal agents are assumed to be either corrupt or honest, with the measure of honest agents equal to À. Upon meeting a corrupt agent, the distributor has to pay a bribe b if he wants this agent to back him in court in case the exporter files a suit to recover his due revenue. With the support of the legal agent, the distributor gets away with a default almost surely (i.e., there is only a small probability ê that support from the legal agent will not deliver victory in

court). By contrast, a defaulting distributor has no chance of winning a legal battle against the exporter if he does not find a corrupt legal agent. Whenever the distributor is defeated in court, he has to pay both the revenue due to the exporter and a fine

f

>

O to the judicial system. Exporters do not observe the possible interactions between distributors and legal agents in Foreign.

3

Exporter's Behavior

We analyze the behavior of exporters by considering a generic partnership between an exporter and a distributor. T'hroughout this section, we assume that a patient distributor never wants to default and a myopic distributor defaults whenever he expects the legal system to fail to enforce contracts, i.e., whenever he finds (and bribes) a corrupt legal agent. In the next section, we prove that this behavior is part of an equilibrium as long as Ód is high enough.

The problem of the exporter is as follows. In every period, he decides whether to maintain the partnership. If he chooses to do so, he writes a one-period contract with the distributor establishing the volume of output to seU in Foreign. We consider first how this quantity is determined.

3.1

Contract

Consider a contract signed at date t and let the exporter's belief that the distributor is myopic be denoted by (J. The exporter pays the cost of production and receives a fraction Q of the revenue if the distributor does not default. There is a probability 1 - (J that the distributor is patient, in

which case we claim that he never defaults. However, if he is myopic, he defaults whenever he does not expect the legal system to enforce his contract, an event with probability 1 - À. In that event,

the exporter receives his fraction of the revenue with probability ê, since it is always optimal for an

always mimic the choice of the patient distributor during the contractual negotiation but may default afterwards. In that case, no constraints on the form of contracts would be required, since contracts could not reveal any information about the distributor's type, which is the condition necessary for reputation to have value in equilibrium.

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l:

exporter to sue the distributor after a default. Under the proposed strategy for the distributors, the exporter's expected profit when the contract establishes a production leveI of q is then

n(q, O; À, ê, a, ｣ＬｾＩ＠ = -cq

+

a[O(À

+

(1-À)ê)

+

1-O]R(q) ＭｾＬ＠ (1)

where R(q) is the revenue from selling q units in Foreign.9

Note that, since the exporter pays the cost of production, the gain of the distributor inside a partnership is always positive. Therefore, a contract never violates the distributor's participation constraint. Moreover, our assumptions on the structure of the contract imply that it cannot be used to extract information about the distributor's type. Hence, given the decision to sign a contract, the exporter's optimal decision is simply to choose q to maximize n(q, O; À, ê, a, c, ｾＩＮ＠ Let

Q

denote this optimal quantity. It depends on the beHef O of the exporter, the institutional parameters À

and ê, the exogenous sharing rule and the marginal cost of production:

Q = Q(O; À, ê, a, c).

Note that the first-order condition for Q to maximize n(q, O) requires R'(Q)

>

O, while the second-order condition requires R"(Q)

<

o.

It follows from equation (1) that the optimal quantity to export, Q, satisfies

ôQ (1 - ê)(I-À)R'(Q)

ôO - [B(À

+

(1 - À)ê)

+

1-O]R"(Q)

<

O.

(2)

Thus, the optimal export quantity expands as the belief that the distributor is myopic decreases. It

also follows from equation (1) that, for a given O, the volume of trade expands when legal stability improves.lO

We assume that parameters À, ê, a and ｾ＠ satisfy the following conditions:

AI Q(I; À, ê, a, c)

>

O

A2 n(Q, 1; À, ê, a, ｣ＬｾＩ＠

<

O

A3 n(Q, O; À, ê, a, ｣ＬｾＩ＠

>

O.

Thus, the quantity that maximizes current variable expected profits is strictly positive even when the exporter is certain that the distributor is myopic

(O

= 1). In that case, however, the exporter's

9Since marginal costs are constant, domestic sales do not affect foreign sales, and vice versa. Notice also that we keep final consumers on the background, dealing directly with revenue functions.

lONote in addition that, if enforcement of contracts is stricter when the involved parties are within the same national jurisdiction, as it appears to be the rule, then exporters will tend to sell more domestically than in foreign markets, in line with the findings in the empiricalliterature on plant-level exporting behavior (see Tybout 2003).

current (total) expected profit is strictly negative. In contrast, when the exporter is certain that the distributor is patient

(O

=

O), his current (total) expected profit is strictly positive.

Given assumptions AI-A3, it is elear that when O = 1, the exporter terminates the partnership and produces only for the domestic economy. Note, however, that the same reasoning does not necessarily hold for values of O elose enough to 1. In that case, even though profits are still negative (since 1f is a continuous function of q and O), it may be optimal to produce because this will generate

additional information about the type of the distributor.

3.2 Information

In every period, the exporter has to decide whether to maintain the partnership with the distributor he is paired with. This decision depends critically on the exporter's belief about the type of the distributor. For example, if he believes that there is a high probability that the distributor will attempt to default on the contract, he willlikely prefer to terminate the partnership.

The exporter updates his belief with respect to the type of the distributor through his experience in the partnership. This experience refiects all previous decisions made by the distributor. Under the proposed strategy for the distributors, if the exporter observes a default, he forms a posterior equal to 1, since he immediately coneludes that the distributor is myopic. Alternatively, if he does not observe a default, he adjusts his belief about the distributor's type according to the Bayes rule:

>'0

O( {no default}, O)

==

Pr(m

I

{no default}

n

O) = >'0

+

1-O

<

O. (3)

Note that the adjustment in O is downwards in this case. That is, when the exporter observes no default, he increases (decreases) his belief that the distributor is patient (myopic).

More generally, let O indicate a record of no default and 1 indicate a record of default in a given experience and define Ot( c) as the belief that the distributor is myopic given an experience ht _with

t

size

t

and cardinality c, where c

==

Lj=l hj, hj E {O, I}. If the distributor follows the strategy specified above, the exporter's belief is given by

e,(c) = { (4) Note that Ot(O) decreases with

t

and converges to zero when

t

goes to infinity.That is, if a distributor never defaults, in the long run the exporter becomes convinced that the distributor is patient. We interpret O as the reputation of the distributor. A reputation of being patient means that the belief O of the exporter regarding the distributor in their partnership is small. Note that all agents outside the partnership hold a common belief 00 that the distributor is myopic, since

they cannot observe the actual experiences inside the partnership.

10

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We now take as given the function

Q

and the updating process described in equation (4) and look at the exporter's decision between maintaining a partnership and terminating it.

3.3 Partnership

Consider an exporter at date

t

facing the decision on whether to maintain a partnership. Since the only new information he accumulates over time comes from his experience with the distributor, each possible experience up to date

t

represents an information set upon which he can base his decision. Moreover, we know from expression (4) that all relevant information in an experience can be captured by the belief B associated with it. Given B, the exporter can compute both the optimal quantity to export and, given the assumed strategy for the distributors, the distribution of the next period's beliefs. These two elements affect, respectively, the flow and the continuation payoff of maintaining a partnership. The flow payoff corresponds to the current profit 7r(B), where

7r(B)

==

-cQ

+

a[B(À

+

(1-À)e)

+

1 - B]R(Q) - K. (5)

To find the continuation payoff of maintaining a partnership, recall that after observing a default, the exporter immediately concludes that the distributor is myopic and updates his posterior to

B = 1. Assumption A2 then implies that the exporter terminates the partnership. Alternatively, if the exporter observes no default, he increases (decreases) his belief that the distributor is patient (myopic). Since the exporter's profit is a decreasing function of B, the exporter does not terminate the partnership in this case.

This reasoning implies that the exporter's expected profit can be described in terms of a value function v( B) as this:ll

v( B) = max {O, 7r( B)

+

b"e Pr(O

I

B)v[B(O, B)]} , (6)

where

Pr(O

I

B) = 1 - B

+

ÀB (7)

is the probability of no default given the belief B. Expression (6) can be interpreted as follows. At every date, if the exporter decides to maintain the partnership, he receives expected profits of 7r(B) and, through his experience, obtains additional information about the distributor's type. Note that this reasoning presumes that an exporter will never attempt to form a new partnership after

llWe do not include domestic profits in v(B), since they do not affect (and are not affected by) the decision on whether to continue the partnership.

11

terminating one. This is a direct consequence of the fact that, after date O, only myopic distributors are avaiIable to form new partnerships.12

Proposition 1 describes the exporter's optimal decision as a function of his beIief ().

Proposition 1 The problem of the exporter has an unique optimal solution. He starts the

part-nership at date O as long as his prior is smaller than ()C, where BC E (0,1). If the exporter observes a default, he terminates the partnership and produces only for the local market from that period on. If the exporter does not observe a default, he maintains the partnership. At any period at which the partnership is active, he chooses to export Q(();)., ê, a, c).

Proof. First, Q(();)., ê, a, c) solves the exporter's maximization problem (1). Hence, it must be

the quantity established in any contract. Assumption A2 and the Bayesian updating in (4) imply that the exporter terminates the partnership after the realization of a default. Moreover, since all ｡ｶ｡ｩｬ｡ｾｬ･＠ qistributors from date 1 on are myopic, an exporter never attempts to form a new

partnership after date O.

Now, to show the existence of the threshold BC, consider the exporter's decision to start a partnership at date O. If he enters the partnership, his expected payoff is

(8)

where v(BI(O» is given by (6) evaluated at () = BI(O). Substituting for V(()I(O)) in (8), we obtain Repeating the same substitution and using expression (7), we can rewrite equation (8) after some manipulation as

00 i-I

v(()o) = 7r(Bo)

+

L

ＸｾＷｲＨＨＩｩＨＰﾻ＠

11

(1-()j(O)

+

).()j(O)).

i=1 j=O

Note that, from expressions (5) and (4),

o7r(()i(O)) = o7r(()i(O) oBi(O) = -a(l- ).)R[Q(Bi(O).;)., ê, a, c)]).i

<

O

o()o oBi(O) oBo (1- ()o

+

).tBO)2 .

i-I

Moreover, each component of

11

(1-()j(O)

+

).()j (O» is also a strict1y decreasing function of Bo. We

j=O

can then conc1ude that, in the domain ()o E [0,1], v(()o) is a strictIy decreasing function. Now, since

v(O) = 7r(0)

>

O

1- 8e

12In Section 6, when we introduce search frictions, the pool of available agents after date O also includes patient distributors.

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by A3 and

ｾＨＱＩ＠

=

7r(1)

o

v 1-6_{e À}

<

by A2, there is a unique value ()C such that

{

ii(())::; O

ii(())

>

O

if ()o :;::: ()C

if ()o

<

()c.

Hence, an exporter enters in a partnership if and only if his prior ()o is below the threshold ()c. •

Throughout the paper, we assume ()o

<

()c. Hence, at date O, alI producers want to form

partnerships and become exporters. Note that the exporter's problem is potentialIy rather com-plex. Exporters need to make a decision after every experience they face, and the set of possible experiences tends to increase as time goes on. The key element in our model that avoids these complications is our assumption that "bad outcomes" from the perspective of exporters are always caused by opportunistic behavior of distributors. This implies that the construction of a good reputation takes time, whereas a bad reputation can be acquired in a single period. The advantage of this simplification is essentialIy that it alIows us to generate precise, clear-cut results on the re-lationship between the history of a partnership and its corresponding volume of trade. We discuss this issue further in Section 5.13

4

Distributor's Behavior and Equilibrium

We now solve the distributor's problem and characterize an equilibrium of the partnership between the exporter and the distributor. Consider first the problem faced by a myopic distributor. By definition, he does not care about the future and thus does not bother to build reputations. Clearly, he does not default when he does not find a legal agent who accepts a bribe, since otherwise he would be forced by the courts to compensate the exporter and to pay an additional penalty fee,

f.

When the distributor finds a corrupt agent, he bribes the agent if and only if he plans to default on the contract. If the distributor does not default, he then simply receives a fraction 1 - a of the revenue. Conversely, if he defaults, he pays the bribe b to the agent and is successful in court with probability 1 - ê, in which case he retains alI the revenue from selling Q. If the distributor loses

13In Araujo and Omelas (2004), we consider the case where exporters may face bad outcomes even when distrib-utors do not behave opportunistically, for example because of a negative demand shock not observed by foreigners. In that case, both good and bad reputations require time to be established. It tums out that the optimal behavior of an exporter also involves a threshold O' such that a partnership is terminated if and only if the posterior O of the exporter becomes higher than 0'. The solution method is, however, more demanding and involves the interpretation of the exporter's problem as a Two-Armed Bandit Problem.

the case in court, he retains only a fraction 1 - a of the revenue and pays the fee

f.

Thus, upon finding a corrupt agent, the distributor chooses to default as long as

(1-e)R[Q(O;.x, e, a, c)]

+

e{(l - a)R[Q(O;.x, e, a, c)]- f} - b

>

(1- a)R[Q(O;.x, e, a, c)].

This inequality can be rewritten as

ef+b

R[Q(O;.x, e, a, c)]

>

a(l _ e)"

We assume henceforth that this inequality is always satisfied. That is, we consider that b,

f,

1-a

and e are small enough to satisfy the following condition:

ef+b

A4 : R[Q(I;

.x,

e, a, c)]

> (

_aI-e

) .

A patient distributor, on the other hand, anticipates that after a default his partnership will be terminated. Hence, as long as he is not too impatient, he does not default. Proposition 2 formalizes this claim.

Proposition 2 There is a value 6d E (0,1) such that, for all _6d

>

_6d, the optimal choice of a patient distributor is to always honor his contract.

Proof. Consider the problem of a patient distributor at some date

t.

He does not deviate from the strategy of never defaulting as long as

00

(l-a)

L

_{Ｘｾｒ｛ｑＨｏｫＨｏＩ［ＮｸＬ＠}

e, a, c)]

>

(I-e)R[Q(Ot(O);.x, e, a, c)]+e{(I-a)R[Q(Ot(O);.x, e, a, c)]-J}-b. k=t

(9)

Now, since

from equation (4) and

ôR[Q(Ot(O);.x, e, a, c)] _ (1 - .x){R'[Q(Ot(O);.x, e, a, c)]}2

<

O

ôOt(O) [1-Ot(O)(I - .x)]R"[Q(Ot(O);.x, e, a, c)]

from equation (2), we know that R(.) is increasing in t. Therefore, a sufficient condition for inequality (9) to hold at any

t

is

(1 - a)R[Q(Oo; À, e, a, c)]

1 _ 6

d

>

(1 - e)R[Q(O;.x, e, a, c)]

+

e{ (1 - a)R[Q(O;.x, e, a, c)] - f} - b.

14

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Since the left-hand side is strictly increasing in Od and goes to infinity when Od approaches 1, there is a Od such that, for all Od

>

Od, the optimal choice of a patient distributor is to always honor his contract . •

We now show that the exporter's behavior described in Proposition 1 and the distributor's behavior described in Proposition 2 are part of an equilibrium.

Proposition 3 Consider the following strategy profile. The exporter always starts a partnership at date O, chooses quantities according to the function Q(Oj.À, e, a, c), and maintains the partnership as long as he observes no default. A myopic distributor defaults if and only if he finds a corrupt legal agent. A patient distributor never defaults. Irrespective of his type, the distributor never terminates the partnership. This profile, together with the Bayesian updating described in equation (4), is a sequential equilibrium.

Proof. If the partnership is terminated, the probability that the distributor will meet another exporter in the future is zero, since the exporters anticipate that the distributors available after

t

= O are all myopic. Therefore, the distributor never wants to separate from the exporter. From Proposition 2, we know that a patient distributor chooses to honor contracts as long as Od

>

Od.

In contrast, myopic distributors default whenever they find a corrupt legal agent, since they just maximize current profit. Note now that, by construction, the exporter's strategy is a best reply to the distributor's strategy. Moreover, it is sequentially rational by the principIe of optimality. Finally, since beHefs are defined by the Bayes' rule after every possible experience, including the ones that are never reached in equilibrium, they are consistent. •

5

Dynamics of Trade

We now show how the volume of trade within a partnership evolves under the equilibrium described in Proposition 3. Note first that, even though the type of a distributor is crucial to determine the probability that a partnership lasts, the actual volume of trade depends only on the distributor's reputation. This is so because there is only one experience that arises with positive probability within an ongoing partnership, i.e., a sequence of no defaults. This feature of the model allows us to concentrate on the evolution of the export volume irrespective of the type of the distributor the exporter is paired with.

Note also that there is a one-to-one correspondence between the distributor's reputation and the time span of the partnership. Therefore, we can obtain a clear relationship between the export volume and the age of the partnership. With some abuse of notation, let Ot

==

Ot(O). Then, since

and, from equation (4),

we obtain

ôQt _ (1-e)(I- À)R'(Qt)

<

O

ôOt [1 - Ot(l- À - (1- À)e)] R"(Qt) ôOt _ Àt In ÀOo(1 - 00 )

<

O

ôt - (Àtoo

+

1 - 00)2 '

dQt _ ôQ ôOt O

dt - ôOt ôt

> .

Hence, in every ongoing partnership, the volume of trade increases over time and converges to

Q(O; À, e, a, c), the leveI reached when contracts are perfectly enforced. This result captures in a

clear way the idea that trust is built over time, through repeated interactions. While an exporter is learning about the type of his partner, he exports less than he would under perfectly enforceable contracts. Thus, in the first stages of a partnership, relatively low quantities are exported; if the distributor appears to be reliable, the exporter then progressively improves the volume exported. This result rationalizes the practice of "start small and increase quantities over time" referred to in the Introduction. If this process continues until the exporter becomes sufficiently convinced that his distributor is patient, the lack of contract enforcement becomes effectively inconsequential. Hence, in line with with the empirical findings of Johnson et al. (2002), sufficiently long-lasting partnerships overcome all problems created by informational frictions.

At any time, the volume of trade within an ongoing partnership is affected also by the in-stitutional setting of the Foreign economy. We study this issue by describing how changes in À

affect current and future contracts between the exporter and the distributor. Suppose that, at the beginning of date

t,

there is an institutional development in Foreign that makes corruption less attractive to legal agents in Foreign-e.g., an increase in the costs of being caught. Assuming that under this new environment fewer agents will accept bribes from distributors, this change will lead to an increase in the proportion of international contracts enforced in Foreign. Let then the resulting institutional parameter be denoted by Àt, where the subscript

t

on À indicates that the change happened at date

t.

Clearly, the immediate effect of this change is an improvement in the volume of trade, just as Johnson et al. (2002) find for partnerships in transition economies:

ôQt -Ot(l- e)R'(Qt) O

ôÀt [1 - Ot(1 - Àt - (1- Àt)e)] R"(Qt)

> .

Since the exporter anticipates that he will receive his share of the total revenue with a higher probability, he is wilEing to export more.

Note that the distributor's reputation at

t

is not affected by the increase in Àt. This is so because reputation is a function of past leveIs of contract enforcement, not the current one. On

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the other hand, the change in >. also affects the future reputation of the distributor. Consider, for example, his reputation at date

t

+

k, k> O. From equation (4), we obtain

80t

H =

>.:-lOt(l

-

Ot)

>

O

8Àt (>';Ot

+

1 - Ot)2 .

Hence, a further implication of the improvement in the institutional setting of Foreign is that it reduces the future reputation of distributors, relative to what they would have been under the lower >.. Intuitively, a higher >. makes it less clear for an exporter that the distributor is complying with the contract voluntarily, rather than motivated by the threat of a legal challenge.

As a result, the net impact of an institutional change in Foreign on future export volumes is not as transparent as its contemporaneous effect is. Consider the case of an improvement in Foreign's ability to enforce international contracts starting at date 0.14 _{We have that, for all}

_t

_>

_O,

(10)

There are two effects in play here. First, an increase in >. has a direct positive effect on exports in period

t

for the same reason it has in date

o.

This effect is represented by the first element in the square bracket of equation (10). But there is also an indirect negative effect due to the slower improvement in the distributor's reputation associated with the increase in >.-represented by the second element in the square bracket of equation (10). The net impact depends on the comparison between these two forces. That is, an increase in >. at date O improves the export volume at date

t

beyond its original trend if and only if

(11)

We can rewrite this inequality as

_

80

t (1->.)

'T](Ot, >.) = - 8(1-À) Ot

<

1,

where 'T](Ot, >.) indicates the date

t

elasticity of the distributor's reputation with respect to a date O change in the institutional setup in Foreign. The intuition is clear: the overall effect of an increase in >. on future export volumes is positive as long as it does not induce large changes in the process of reputation building.

Using equation (4), inequality (11) can be written also as

>. 1 - 0₀(1 _

>.t)

t<--

.

1->. 1 - 0₀

(12)

14This restriction is made only for notational simplicity; the result is analogous if the permanent increase starts at some date t > Q.